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The Behavior of Gases

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Compressibility Gases can expand to fill its container, unlike solids or liquids The reverse is also true: They are easily compressed, or squeezed into a smaller volume

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Compressibility This is the idea behind placing air bags in automobiles In an accident, the air compresses more than the steering wheel or dash when you strike it The impact forces the gas particles closer together, because there is a lot of empty space between them.

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Variables that describe a Gas The four variables: ( STP) 1. Pressure (P) in kilopascals, 760 mmHg, 760 Torr, and 1 Atm 2. Volume (V) in Liters, ml 3. Temperature (T) in 273 Kelvin 4. Amount (n) in moles

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Volume Pressure Temperature Amount of space enclosed by a shape or object Force exerted on a surface per unit area. Measure of the average heat or thermal energy of the particles in a substance.

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1. Amount of Gas When we inflate a balloon, we are adding gas molecules. Increasing the number of gas particles increases the number of collisions thus, the pressure increases If temperature is constant, then doubling the number of particles doubles the pressure

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2. Volume of Gas In a smaller container, the molecules have less room to move. The particles hit the sides of the container more often. As volume decreases, pressure increases. (think of a syringe) Thus, volume and pressure are inversely proportional to each other

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3. Temperature of Gas Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly proportional) The molecules hit the walls harder, and more frequently!

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1. The volume of a gas particle is miniscule compared to the distance between themselves and other molecules. 2. Gas particles undergo no intermolecular attractions or repulsions. 3. Gas particles are in continuous, random motion. 4. Collisions between gas particles are perfectly elastic. 5. The average kinetic energy is the same for all gases at a given temperature, regardless of the identity of the gas.

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The Gas Laws

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Robert Boyle ( )

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Boyles Law Equation: P 1 V 1 = P 2 V 2 Gas pressure is inversely proportional to the volume, when temperature is held constant.

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Graph of Boyles Law – page 418 Boyles Law says the pressure is inverse to the volume. Note that when the volume goes up, the pressure goes down

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A balloon contains 7.2 L of He. The pressure is reduced to 2.00 atm and the balloon expands to occupy a volume of 25.1 L. What was the initial pressure exerted on the balloon?

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Jacques Charles ( )

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Charless Law The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant. Temperature Must Be in Kelvin.

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Converting Celsius to Kelvin Gas law problems involving temperature will always require that the temperature be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.) Kelvin = C °C = Kelvin - 273

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A balloon is filled with 3.0 L of helium at 310 K. The balloon is placed in an oven where the temperature reaches 340 K. What is the new volume of the balloon?

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Joseph Louis Gay-Lussac (1778 – 1850)

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Gay-Lussacs Law The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.

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#4. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

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The equation for Avogadro's Law is V/n=k. V is the volume of the gas, n is the amount of substance of the gas, and k is a proportionality constant.

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5.00 L of a gas is known to contain mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?

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Daltons Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P P 1 represents the partial pressure, or the contribution by that gas. Daltons Law is particularly useful in calculating the pressure of gases collected over water.

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If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3: 2 atm + 1 atm + 3 atm = 6 atm Sample Problem 14.6, page

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8. Grahams Law The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Derived from: Kinetic energy = 1/2 mv 2 m = the molar mass, and v = the velocity. Rate A Mass B Rate B Mass A =

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Ideal Gas Law

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The Ideal Gas Law Equation: P x V = n x R x T Pressure times Volume equals the number of moles (n) times the Ideal Gas Constant (R) times the Temperature in Kelvin. R=.0821

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What volume is occupied by 5.03 g of O2 at 28°C and a pressure of 422 mmHg?

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Density Density is mass divided by volume m V so, m M P V R T D = =

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Ideal Gases dont exist, because: Molecules do take up space There are attractive forces between particles - otherwise there would be no liquids formed

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Real Gases behave like Ideal Gases... When the molecules are far apart. The molecules do not take up as big a percentage of the space We can ignore the particle volume. This is at low pressure

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Real Gases behave like Ideal Gases… When molecules are moving fast This is at high temperature Collisions are harder and faster. Molecules are not next to each other very long. Attractive forces cant play a role.

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Diffusion is: Effusion: Gas escaping through a tiny hole in a container. Both of these depend on the molar mass of the particle, which determines the speed. u Molecules moving from areas of high concentration to low concentration. u Example: perfume molecules spreading across the room.

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Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Molecules move from areas of high concentration to low concentration. Fig , p. 435

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Effusion: a gas escapes through a tiny hole in its container -Think of a nail in your car tire… Diffusion and effusion are explained by the next gas law: Grahams

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Sample: compare rates of effusion of Helium with Nitrogen – done on p. 436 With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases! Grahams Law

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